It sounds like you are asking what the maximum current a Zumo shield might draw is. We do not have some maximum figure well characterized, and how much your robot draws will be heavily dependent on your application. By far, the motors will draw the majority of the current. You should note that the reverse protected battery voltage is given to the motors, so if you plan to connect your 8.4V battery to the charge port on the shield, the motors will get 8.4V. As a result the motors will run faster and draw more current than they would with the standard AA batteries. Driving them at the higher voltage will also reduce their lifetime.

Thank you for the reply. My main concern was the extra voltage that will bypass the onboard regulator and be dumped into the sensors. I know the motors consume ~1.2 amps max, so I thinking a 5a Buck “should” be enough. Time will tell.

The front sensor array for the Zumo for Arduino is supplied by the 7.4V step-up regulator on-board. If you connect an 8.4V battery, the output of that regulator will match the battery voltage rather than actually be regulated, so the LEDs on the front sensors will be brighter. This might affect their performance in tasks like line following.

Even with the increased current draw of the motors from the increased voltage, a regulator that can output 5A seems like it should be fine.